Skip to content

Opening book details…

Can I read Optimal lower bounds for cubature error on the sphere S2 on EtoBox?

Optimal lower bounds for cubature error on the sphere S2 by Kerstin Hesse; Ian H. Sloan is a Mathematics article available to read on EtoBox.

What is Optimal lower bounds for cubature error on the sphere S2 about?

We show that the worst-case cubature error E(Q m ; H s ) of an m-point cubature rule Q m for functions in the unit ball of the Sobolev space H s =H s (S 2 ), s > 1, has the lower bound E(Q m ; H s ) c s m -s 2 , where the constant c s is independent of Q m and m. This lower bound result is optimal, since we have established in previous work that there exist sequences 2 with a constant cs independent of n. The method of proof is constructive: given the cubature rule Q m , we construct explicitly a 'bad'function f m ∈ H s , which is a function for which Q m f m =0 and f m -1 The construction uses results about packings of spherical caps on the sphere.

Who reads Optimal lower bounds for cubature error on the sphere S2?

It is typically read by researchers, students, and practitioners in Mathematics.

Author
Kerstin Hesse; Ian H. Sloan
Publisher
Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0885-064X)
Published
2005
Language
EN
Field
Mathematics (Physical Sciences)

More by Kerstin Hesse; Ian H. Sloan

Browse all works by Kerstin Hesse; Ian H. Sloan